Free ideal ring
Definition for commutative rings
Symbol-free definition
A commutative unital ring (or any commutative ring) is termed a free ideal ring or fir if every ideal of that ring is a free module as a module over that ring.
Definition for noncommutative rings
For noncommutative rings, there are two notions:
- Free left ideal ring or left fir
- Free right ideal ring or right fir